Systems and methods of range tracking

ABSTRACT

Systems include at least one electronic waveform processor operatively associated with at least one reflected signal electronic sensor and configured and programmed to generate an estimate of the range from an object to a target and an estimate of the closing velocity of the object to the target using a reflected signal. Systems use a non-linear swept electromagnetic FM signal.

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

The invention described herein may be manufactured and used by or forthe government of the United States of America for governmental purposeswithout the payment of any royalties thereon or therefor.

FIELD OF THE INVENTION

Embodiments of the invention generally relate to a radar system and/ormethod for tracking a target using a plurality of modules

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram of an embodiment of modules used in anActive-Mode embodiment of the invention that uses a quadratic derivativemodule.

FIG. 2 is a block diagram of an embodiment of modules used in anActive-Mode embodiment of the invention that uses a quadratic regressionmodule.

FIG. 3 is a block diagram of an embodiment of modules used in anSemi-Active-Mode embodiment of the invention that uses a quadraticderivative module.

FIG. 4 is a block diagram of an embodiment of modules used in anSemi-Active-Mode embodiment of the invention that uses a quadraticregression module.

FIG. 5 illustrates a block diagram of an embodiment of an electronicwaveform processor, including at least some of the processor'sassociated components as described in the Detailed Description.

It is to be understood that the foregoing and the following detaileddescription are exemplary and explanatory only and are not to be viewedas being restrictive of the invention, as claimed. Further advantages ofthis invention will be apparent after a review of the following detaileddescription of the disclosed embodiments, which are illustratedschematically in the accompanying drawings and in the appended claims.

DETAILED DESCRIPTION

Embodiments of the invention generally relate to a radar system and/ormethod for tracking a target. Embodiments of the invention include anelectronic transmitter adapted to emit a non-linear sweptelectromagnetic FM signal. The non-linear swept electromagnetic FMsignal has a waveform mathematically described by asecond-order-polynomial.

In some embodiments, the non-linear swept electromagnetic FM signal istransmitted from an electronic transmitter electromechanicallyassociated with an object other than the object for which a range (to atarget) and/or closing velocity (to the target) will be estimated. Inthese embodiments, the object with which the electronic transmitter iselectromechanically associated could be any object, such as, forexample, a vehicle, such as an aircraft (including an UAV), water-goingvessel, or land-going vessel. In these embodiments, an ‘apparent emittedsignal electronic sensor’ associated with the object whose range andclosing velocity to a target will be estimated is adapted to receive a‘semi-active mode apparent emitted signal’. The ‘semi-active modeapparent emitted signal’ corresponds to the non-linear sweptelectromagnetic signal emitted from the electronic transmitter. In theseembodiments, an electronic waveform processor is operatively associatedwith the ‘apparent emitted signal electronic sensor’ such that theelectronic waveform processor can electronically process the‘semi-active mode apparent emitted signal’ received by the ‘apparentemitted signal electronic sensor’. With reference to FIG. 5, as used inthis specification including the claims, an ‘electronic waveformprocessor’ 500 includes a CPU 502, of any physical form, and computermemory 504 on which a sequence(s) of instructions executable by the CPUis/are stored; a sequence of stored instructions is referred to as a‘module’ and the CPU is adapted to execute the ‘modules’.

In other embodiments, the non-linear swept electromagnetic FM signal isemitted from an electronic transmitter electromechanically associatedwith the object for which a range and/or closing velocity will beestimated. In these embodiments, the non-linear swept electromagnetic FMsignal emitted from the electronic transmitter is communicated to theelectronic waveform processor that is operatively associated with theelectronic transmitter via a guided transmission medium/media; thenon-linear swept electromagnetic FM signal emitted from the electronictransmitter via the guided transmission medium/media corresponds to thenon-linear swept electromagnetic FM signal emitted from the electronictransmitter and is referred to in this specification including theclaims as a ‘active mode emitted signal’.

The term ‘apparent emitted signal’ is used in this specificationincluding the claims to describe the signal corresponding to the emittednon-linear swept electromagnetic FM signal (‘semi-active mode apparentemitted signal’ and/or ‘active mode apparent emitted signal’) that isprovided to the electronic waveform processor and is intended tosimulate the actual non-linear swept electromagnetic FM signal emittedby the electronic transmitter. Table 1 provides definitions of variablesused in Tables 2, 3, 4, 5, 6, and/or 7.

TABLE 1 Variable Definitions light = speed of light in feet/secondtime_in_sweep = time since beginning of sweep, in seconds a = see FIG. 6b = see FIG. 6 c = see FIG. 6 d = see FIG. 6 k = see FIG. 6 A1 = firstsweep's value of A A2 = second sweep's value of A B1 = first sweep'svalue of B B2 = second sweep's value of B period = length of timebetween each digitized sample Velprev = value of velocity at previoussample time Accprev = value of acceleration at previous sample time${{KN}\; 1} = \frac{N}{{delk}*\left( {{N{\sum\limits_{i = 1}^{N}\left( i^{2} \right)}} - \left( {\sum\limits_{i = 1}^{N}i} \right)^{2}} \right)}$${{KN}\; 2} = \frac{\sum\limits_{i = 1}^{N}i}{{delk}*\left( {{N{\sum\limits_{i = 1}^{N}\left( i^{2} \right)}} - \left( {\sum\limits_{i = 1}^{N}i} \right)^{2}} \right)}$$\frac{1}{Kdop}$$\frac{{delk}*\left( {{\sum\limits_{i = 1}^{N}i} - N} \right)}{N*{Kdop}}$$\frac{1}{N*{Kdop}}$$\frac{N}{{delk}*\left( {{N{\sum\limits_{i = 1}^{N}\left( i^{2} \right)}} - \left( {\sum\limits_{i = 1}^{N}i} \right)^{2}} \right)}$$\frac{\sum\limits_{i = 1}^{N}i}{{delk}*\left( {{N{\sum\limits_{i = 1}^{N}\left( i^{2} \right)}} - \left( {\sum\limits_{i = 1}^{N}i} \right)^{2}} \right)}$

Embodiments further include at least one ‘reflected signal electronicsensor’ (not illustrated) adapted to receive the semi-active modeapparent emitted signal and associated with an object whose range andclosing velocity to a target will be estimated. At least one of the atleast one ‘reflected signal electronic sensor’ is adapted to receive a‘reflected signal’; the ‘reflected signal’ corresponds to the non-linearswept electromagnetic signal emitted from the electronic transmitter andhaving been reflected from the target.

Embodiments further include at least one electronic waveform processoroperatively associated with the at least one ‘reflected signalelectronic sensor’ and configured and programmed to process the‘apparent emitted signal’ and the ‘reflected signal’ to generate anestimate of the range from the object to the target and an estimate ofthe closing velocity of the object to the target.

With reference to FIGS. 1-4, the electronic waveform processor includesa CPU and a plurality of modules (100, 200, 300, 400) executablyassociated with the CPU.

With reference to FIGS. 1-4, in some embodiments, the plurality ofmodules includes at least one ‘Emitted Signal Characteristics’ module 2a, 2 b. When run by the electronic waveform processor, the ‘EmittedSignal Characteristics’ module 2 a, 2 b causes the electronic waveformprocessor to calculate predetermined characteristics of the ‘apparentemitted signal’. The predetermined characteristics of the non-linearswept electromagnetic signal include, but not limited to: 1) an expectedfrequency change in the ‘apparent Doppler shift’ (between the apparentemitted signal and ‘reflected signal’) with respect to change in closingvelocity—this characteristic referred to in this specification includingthe claims as ‘kdop’; 2) an expected frequency change in the ‘apparentDoppler shift’ with respect to change in range from the object to thetarget—this characteristic referred to in this specification includingthe claims as ‘krng’; and 3) expected rate of change of ‘krng’ during agiven FM sweep—this characteristic referred to in this specificationincluding the claims as ‘delkrng’. ‘apparent Doppler shift’ is describedby Equation 1.apparent Doppler shift=Krng*Rng−Kdop*Vel,  Equation 1where ‘Krng’ and ‘Kdop’ are as defined in the preceding paragraph, ‘Rng’is the distance from the object to the target, and ‘Vel’ is the closingvelocity of the object to the target.

Any method of solving for Krng, Kdop, and Delkrng may be implementedthrough the ‘Emitted Signal Characteristics’ module 2 a, 2 b inaccordance with the principles of the invention. The ‘Emitted SignalCharacteristics’ module 2 a, 2 b includes instructions for causing theelectronic waveform processor to calculate values for the variables a,b, c, and d; the Emitted Signal Characteristics module 2 a, 2 b alsocontains instructions for causing the electronic waveform processor toderive Krng, Kdop, and Delkrng using the mathematical relationshipsdescribed in the equations in Table 2.

TABLE 2 Krng, Kdop, Delkrng  Krng = [(−2/light) * (A * time_in_sweep +b)]  A = a + 2d, B = d * k + b, C = c  Krng = [(−2/light) * ((a + 2d) *time_in_sweep + d * k + b)] Note that for non-changing average Krng, d =0, and the above equation reverts to:  Krng = [(−2/light) * (a *time_in_sweep + b)], as expected.  delKrng = −2/light * (a + 2 * d) *Period  Kdop = 2/light * Rearfreqdbl

For illustrative purposes, two ways of solving for the a, b, c, and dvariable values that can be implemented through the ‘Emitted SignalCharacteristics’ module 2 are presented. The first described way isreferred to as a ‘Quad Regression’ module 2 b in FIGS. 2 and 4, whichuses quadratic regression and is described in Table 3.

TABLE 3 Quadratic Regression In the following equation, “b” is timedependent:  Freq_rear = 1/2 * a * time_in_sweep{circumflex over ( )}2 +(d * time + b) *  time_in_sweep + c But during a given sweep, time =time_in_sweep + k:  Freq_rear = 1/2 * a * time_in_sweep{circumflex over( )}2 + [d * (time_in_sweep + k) + b] *  time_in_sweep + c  Freq_rear =1/2 * (a + 2* d) * time_in_sweep{circumflex over ( )}2 + (d * k + b) * time_in_sweep + c  Freq_rear = 1/2 * A * time_in_sweep{circumflex over( )}2 + B * time_in_sweep + C Where  A = a + 2d, B = d * k + b, C = cUsing polynomial regression, can find A, B and C; then, from twoconsecutive sweeps A, B and C values, can calculate the rest:  A1 = a +2 * d  B1 = d * k1 + b  B2 = d * k2 + b Now solving for a, b, c and d: d = (B1 − B2)/(k1 − k2)  a = A1 − 2 * d or a = A2 − 2 * d  b = B1 − d *k1 or b = B2 − d * k2  c = C

The second described way of solving for the a, b, c, and d variablevalues that can be implemented in the ‘Emitted Signal Characteristics’module is referred to as ‘Quad Deriv’ module 2 a in FIGS. 1 and 3, usesquadratic derivation, and is described in Table 4.

TABLE 4 Quadratic Derivation For better range and vel discrimination,illuminator can make “b” time dependent:  Freq_rear = ½ * a *time_in_sweep{circumflex over ( )}2 + (d * time + b) *  time_in_sweep +c But during a given sweep, time = time_in_sweep + k:  Freq_rear = ½ *a * time_in_sweep{circumflex over ( )}2 +[d * (time_in_sweep + k) + b] * time_in_sweep + c  Freq_rear = ½ * (a + 2 * d) *time_in_sweep{circumflex over ( )}2 +(d * k +b) *  time_in_sweep + c Freq_rear = ½ * A * time_in_sweep{circumflex over ( )}2 + B *time_in_sweep + C Where A = a + 2d, B = d * k + b, C = c From 1st and2nd derivatives of Freq_rear, can find A, B and C:$~{A = \frac{d^{2}({Freq\_ rear})}{\left( {d\left( {{time\_ in}{\_ sweep}} \right)}^{2} \right)}}$$~{B = {\frac{d({Freq\_ rear})}{d\left( {{time\_ in}{\_ sweep}} \right)} - {A*\left( {{time\_ in}{\_ sweep}} \right)}}}$then, from two consecutive sweeps A, B values, can calculate the rest: A1 = a + 2 * d  B1 = d * k1 + b, B2 = d * k2 + b Now solving for a, b,c and d:  d = (B1 − B2)/(k1 − k2)  a = A1 − 2 * d or a = A2 − 2 * d  b =B1− d * k1 or b = B2 − d * k2  c = C

With reference to FIGS. 1-4, some embodiments of the invention furtherinclude at least one ‘Doppler Adjust’ module 4. When executed by theelectronic waveform processor, the ‘Doppler Adjust’ module 4 causes theat least one electronic waveform processor to generate an AdjustedDoppler function for at least one sweep; the Adjusted Doppler functionrepresents an adjusted Doppler shift derived using a non-varying rangevalue. In usage, the range and closing velocity are commonly not quiteconstant during a sweep. However, feedback from the past values can beused to “linearize” the equations in FIG. 8 so that then-current valueof range and vel (at index value N) can be solved with linearregression. In some embodiments, the non-varying range value is therange value of the last sample in the at least one sweep. The equationsin Table 5 describe the process used to linearize the equations; theresulting Adjusted Doppler during the sweep, which, when ‘linearlyregressed’ using the ‘Linear Regression’ module, is a line which has aslope and intercept. Solving for slope and intercept thus solves for Rngand Vel.

TABLE 5 Doppler Adjust Krng(i) = [(−2/light) * (a * time_in_sweep + b)]Doppler(i) = Krng(i) * Rng − Kdop * Vel  (i ranges from 1 to N and N =number of samples in a sweep)  Doppler(i) = Krng(i) * Rng(i) − Kdop *Vel(i)  (since Rng and Vel  change slightly during sweep) Canapproximate values of Rng(i) and Vel(i) by integrating from previousvalues:  time_samp = (N − i) * period  Rng(N) = Rng(i) + Velprev *time_samp + 1/2 * Accprev * time_samp{circumflex over ( )}2  Vel(N) =Vel(i) + Accprev * time_samp  Doppler(i) = Krng(i) * [Rng(N) − Velprev *time_samp - 1/2 * Accprev *  time_samp{circumflex over ( )}2]    −Kdop * [Vel(N) − Accprev * time_samp] Making a new adjusted version ofDoppler  Doppler_adj(i) = Doppler(i) + Krng(i) * [Velprev * time_samp +1/2 *  Accprev * time_samp{circumflex over ( )}2]     − Kdop * Accprev *time_samp  Doppler_adj(i) = Krng(i) * Rng(N) − Kdop *Vel(N)  (linearized, to  solve for Rng(N) and Vel(N))

Embodiments further include a ‘Linear Regression’ module 6 in FIGS. 1-4.When executed by the electronic waveform processor, the LinearRegression module 6 causes the at least one electronic waveformprocessor to perform linear regression on the Adjusted Doppler functionto produce a best-fit Linearly Regressed function, the slope of saidLinearly Regressed function representing a first estimate of the rangeof said object to said target; the y-intercept of said LinearlyRegressed function, when divided by the frequency change in the apparenttarget return Doppler with respect to change in range to said target,represents a first estimate of closing velocity of said object to saidtarget; the variance of said best-fit Linearly Regressed functionrepresenting Doppler variance. Equations in Tables 6a and 6b provideequations for solving for the range, slope, range variance, and slopevariance, using linear regression.

TABLE 6a Linear Regression  Doppler_adj(i) = Krng(i)* Rng(N) − Kdop *Vel(N) Line arregression is used to solve the above for Rng(N)andVel(N),which are the latest Rng and Vel estimates:  ${{Rng}(N)} = \frac{{N{\sum\limits_{i = 1}^{N}{{{Krng}(i)}*{Doppler\_ adj}(i)}}} - {\sum\limits_{i = 1}^{N}{{{Krng}(i)}*{\sum\limits_{i = 1}^{N}{{Doppler\_ adj}(i)}}}}}{{N{\sum\limits_{i = 1}^{N}\left( {{Krng}(i)} \right)^{2}}} - \left( {\sum\limits_{i = 1}^{N}{{Krng}(i)}} \right)^{2}}$Since the values of Krng(i) are evenly spaced,by a value of delk, can bewritten  ${{Rng}(N)} = \frac{{N{\sum\limits_{i = 1}^{N}{\left( {{{Krng}(1)} + {\left( {i - 1} \right)*{delKrng}}} \right)*{Doppler\_ adj}(i)}}} - {\sum\limits_{i = 1}^{N}{\left( {{{Krng}(1)} + {\left( {i - 1} \right)*{delKrng}}} \right)*{\sum\limits_{i = 1}^{N}{{Doppler\_ adj}(i)}}}}}{{N{\sum\limits_{i = 1}^{N}\left( {{{Krng}(1)} + {\left( {i - 1} \right)*{delKrng}}} \right)^{2}}} - \left( {\sum\limits_{i = 1}^{N}\left( {{{Krng}(1)} + {\left( {i - 1} \right)*{delKrng}}} \right)} \right)^{2}}$Simplifying :${{Rng}(N)} = {{\frac{N}{{delKrng}*\left( {{N{\sum\limits_{i = 1}^{N}\left( i^{2} \right)}} - \left( {\sum\limits_{i = 1}^{N}i} \right)^{2}} \right)}*{\sum\limits_{i = 1}^{N}\left( {i*{Doppler\_ adj}(i)} \right)}} - {\frac{\sum\limits_{i = 1}^{N}i}{{delKrng}*\left( {{N{\sum\limits_{i = 1}^{N}\left( i^{2} \right)}} - \left( {\sum\limits_{i = 1}^{N}i} \right)^{2}} \right)}*{\sum\limits_{i = 1}^{N}{{Doppler\_ adj}(i)}}}}$Or:${{Rng}(N)} = {{{KN}\; 1*{\sum\limits_{i = 1}^{N}\left( {i*{Doppler\_ adj}(i)} \right)}} - {{KN}\; 2*{\sum\limits_{i = 1}^{N}{{Doppler\_ adj}(i)}}}}$

TABLE 6b Linear Regression${{Vel}(N)} = {\frac{- 1}{Kdop}*\left( {\frac{\sum\limits_{i = 1}^{N}{{Doppler\_ adj}(i)}}{N} - {{{Rng}(N)}*\frac{\sum\limits_{i = 1}^{N}{{Krng}(i)}}{N}}} \right)}$${{Vel}(N)} = {\frac{- 1}{Kdop}*\left( {\frac{\sum\limits_{i = 1}^{N}{{Doppler\_ adj}(i)}}{N} - {{{Rng}(N)}*\frac{\sum\limits_{i = 1}^{N}\left( {{{Krng}(1)} + {\left( {i - 1} \right)*{delk}}} \right)}{N}}} \right)}$${{Vel}(N)} = {{\frac{1}{Kdop}*{{Krng}(1)}*{{Rng}(N)}} + {\frac{{delK}*\left( {{\sum\limits_{i = 1}^{N}i} - N} \right)}{N*{Kdop}}*{{Rng}(N)}} - {\frac{1}{N*{Kdop}}*{\sum\limits_{i = 1}^{N}{{Doppler\_ adj}(i)}}}}$Or:${{Vel}(N)} = {{{KN}\; 1\; V*{{Krng}(1)}*{{Rng}(N)}} + {{KN2V}*{{Rng}(N)}} - {{KN}\; 3\; V*{\sum\limits_{i = 1}^{N}{{Doppler\_ adj}(i)}}}}$

Embodiments further include a ‘Variance’ module 8 in FIGS. 1-4. When runby the electronic waveform processor, the ‘Variance’ module 8 causes theelectronic waveform processor to produce an estimate of variance of thefirst estimate of range of the object to the target using a mathematicalrelation of measured Doppler to range. One mathematical relation of themeasured Doppler to range, and the corresponding relation of themeasured Doppler variance to range variance, is given by the equationsin Table 7.

TABLE 7 Variance  ${{{{{{Rng}(N)} = {{{KN}\; 1*{\sum\limits_{i = 1}^{N}\left( {i*{Doppler\_ adj}(i)} \right)}} - {{KN}\; 2*{\sum\limits_{i = 1}^{N}{{Doppler\_ adj}(i)}}}}}{{{Rng\_ dot}(N)} = {\sum\limits_{i = 1}^{N}{{Doppler\_ adj}(i)*\frac{\partial{{Rng}(N)}}{{\partial{Doppler\_ adj}}(i)}}}}}}{Doppler\_ adj}(i)} = {{Doppler\_ adj}{\_ mean}(i)}$ Rng_dotm(N) = Rng_dot(N)|Doppler_adj(i) = 0, (Doppler_adj(i))² =Doppler_variance  Rng_mean(N) = Rng_dotm(N) + Rng(N)|Doppler_adj(i) =Doppler_adj_mean(i)  ${{Rng\_ mean}(N)} = {{{KN}\; 1*{\sum\limits_{i = 1}^{N}\left( {i*{Doppler\_ adj}{\_ mean}(i)} \right)}} - {{KN}\; 2*{\sum\limits_{i = 1}^{N}{{Doppler\_ adj}{\_ mean}(i)}}}}$ Rng_variance(N) = (Rng_dot(N))² |Doppler_adj(i) = 0, (Doppler_adj(i))²= Doppler_variance - Rng_dotm(N)²  ${{Rng\_ variance}(N)} = {{Doppler\_ variance}*\left( {{{KN}\; 1^{2}{\sum\limits_{i = 1}^{N}i^{2}}} - {2*{KN}\; 1*{KN}\; 2{\sum\limits_{i = 1}^{N}i}} + {N*{KN}\; 2^{2}}} \right)}$

The Variance module 8 in FIGS. 1-4, when executed by the electronicwaveform processor, further causes the electronic waveform processor toproduce an estimate of variance of the first estimate of closingvelocity of the object to the target using a mathematical relation ofmeasured Doppler to closing velocity. One mathematical relation of themeasured Doppler to closing velocity, and the corresponding relation ofthe measured Doppler variance to closing velocity variance, is given bythe equations in Table 8.

TABLE 8 Variance  ${{{{{{{{{{{{Vel}(N)} = {{{KN}\; 1V*{{Krng}(1)}*{{Rng}(N)}} + {{KN}\; 2\; V*{{Rng}(N)}} - {{KN}\; 3V*{\sum\limits_{i = 1}^{N}{{Doppler\_ adj}(i)}}}}}{{{Vel\_ dot}(N)} = {\sum\limits_{i = 1}^{N}{{Doppler\_ adj}(i)*\frac{\partial{{Vel}(N)}}{{\partial{Doppler\_ adj}}(i)}}}}}}{Doppler\_ adj}(i)} = {{{Doppler\_ adj}{\_ mean}(i)} + {{{Krng}(1)}*\frac{\partial{{Vel}(N)}}{\partial{{Krng}(1)}}}}}}{{Krng}(1)}} = {{{Krng\_ mean}(1)} + {{Rng}(N)*\frac{\partial{{Vel}(N)}}{\partial{{Rng}(N)}}}}}}{{Rng}(N)}} = {{Rng\_ mean}(N)}$ Vel_dotm(N) = Vel_dot(N)|Dop, Krng, Rng = 0; (Dop)², (Krng)², (Rng)² =Doppler_variance,  Krng_variance, Rng_variance  Vel_mean(N) =Vel_dotm(N) +Vel(N)|Dop, Krng, Rng = Doppler_mean, Krng_mean, Rng_mean  ${{Vel\_ mean}(N)} = {{{KN}\; 1\; V*{Krng\_ mean}(1)*{Rng\_ mean}(N)} + {{KN}\; 2\; V*{Rng\_ mean}(N)} - {{KN}\; 3\; V*{\sum\limits_{i = 1}^{N}{{Doppler\_ adj}{\_ mean}(i)}}}}$ Vel_variance(N) = (Vel_dot(N)) ²|Dop, Krng, Rng = 0; (Dop)², (Krng)²,(Rng)² = Doppler_variance, Krng_variance, Rng_variance − Vel_dotm(N) ² Vel_variance(N) = KN 1V² * (Krng_mean ² * Rng_variance +Krng_variance *Rng_mean² +  Krng_variance * Rng_variance) + KN2V² * Rng_variance + 5 *KN3V² * Doppler_variance +  2 * KN1V * KN2V * Krng_mean * Rng_variance

Some embodiments further include at least one ‘Refining’ module 10 inFIGS. 1-4. When run by the electronic waveform processor, the Refiningmodule 10 causes the electronic waveform processor to produce a refinedestimate of range and a refined estimate of closing velocity using thefirst estimate of range of the object to the target, the first estimateof closing velocity of the object to the target, the estimate ofvariance of the first estimate of range, and the estimate of variance ofthe first estimate of closing velocity. In some embodiments, theRefining module 10 is a Kalman filter. The Kalman filter refines therange and closing velocity estimates via a least-error estimation of thetrue signal's value when corrupted by noise. The estimates of range andclosing velocity noise are simply their respective variance estimates,and are used to determine the most probable target range, closingvelocity and acceleration.

Some embodiments further include computer readable instructions referredto herein as ‘Dop Com’ module 12. When executed by the electronicwaveform processor, the ‘Dop Com’ module 12 causes the electronicwaveform processor to provide an estimated prediction of where inDoppler frequency the target will appear at the next instant of timefrom next time values of Krng, Rng Kdop and Vel using Equation 2.Dop_comm=Krng*Rng−Kdop*Vel  Equation 2The estimated prediction being derived from a next predicted sweep valueand the next predicted range and closing velocity from object to target.The estimated prediction of where in Doppler frequency the target willappear allows the object to position its Doppler frequency tracker tothe next frequency location in preparation to acquire the next targetsignal sample.

Method embodiments include: transmitting a non-linear sweptelectromagnetic FM signal, using a transmitter; receiving a reflectedsignal at a reflected signal electronic sensor electromechanicallyassociated with the object, the reflected signal corresponding to thenon-linear swept electromagnetic FM signal having been reflected from apredetermined target; and generating an estimate of the range from theobject to the predetermined target and an estimate of the closingvelocity of the object and the predetermined target by electronicallyprocessing the reflected signal received at the second electronic sensorand an apparent emitted signal corresponding to the non-linear sweptelectromagnetic signal emitted from the transmitter received at thefirst electronic sensor.

Some method embodiments include generating an estimate of the range fromthe object to the predetermined target and an estimate of the closingvelocity of the object and the predetermined target by electronicallyprocessing, on an electronic waveform processor, the reflected signalreceived at the second electronic sensor and the apparent emitted signalcorresponding to the non-linear swept electromagnetic signal emittedfrom the transmitter received at the first electronic sensor comprisesrunning a Quad Regression module on the electronic waveform processor,the Quad Regression module causing the at least one electronic waveformprocessor to calculate predetermined aspects of the non-linear sweptelectromagnetic signal emitted from the electronic transmitter, whereinthe predetermined aspects of the non-linear swept electromagnetic signalemitted from the electronic transmitter includes: an expected frequencychange in the ‘apparent Doppler shift’ with respect to change in closingvelocity [kdop]; an expected frequency change in the ‘apparent Dopplershift’ with respect to change in range from the object to the target[krng]; and expected rate of change of the frequency change in the‘apparent Doppler shift’ with respect to change in range to the target(the rate of change being a linear function) [delkrng].

Some method embodiments further include running a Doppler Adjust moduleon the electronic waveform processor; when run, the Doppler Adjustmodule causing the at least one electronic waveform processor togenerate an Adjusted Doppler function for at least one sweep; theAdjusted Doppler function represents an adjusted Doppler shift derivedusing a non-varying range value. In some embodiments, the non-varyingrange value is the range value of the last sample in the at least onesweep.

Some method embodiments further include running a Linear Regressionmodule on the electronic waveform processor; when run, the LinearRegression module causing the at least one electronic waveform processorto perform linear regression on the Adjusted Doppler function to producea best-fit Linearly Regressed function, the slope of the LinearlyRegressed function representing a first estimate of the range from theobject to the target; the y-intercept of the Linearly Regressedfunction, when divided by the frequency change in the apparent targetreturn Doppler with respect to change in range to the target,representing a first estimate of closing velocity of the object to thetarget; the variance of measured Doppler data around the best-fitLinearly Regressed function representing Doppler variance.

Some method embodiments further include running a Variance module on theelectronic waveform processor; when run by the electronic waveformprocessor, the Variance module causes the electronic waveform processorto provide an estimated variance of the first estimate of range of theobject to the target using a mathematical relation of measured Dopplerto range and an estimate of variance of the first estimate of closingvelocity of the object to the target using a mathematical relation ofmeasured Doppler to closing velocity.

Some method embodiments further include running at least one RefiningModule; when run by the electronic waveform processor, the Refiningmodule causing the electronic waveform processor to produce a refinedestimate of range and a refined estimate of closing velocity using thefirst estimate of range from the object to the target, the firstestimate of closing velocity of the object and the target, the estimateof variance of the first estimate of range, and the estimate of varianceof the first estimate of closing velocity.

Some method embodiments further include running at least one Dop Commodule; when run by the electronic waveform processor, the Dop Commodule causing the electronic waveform processor to provide an estimatedprediction of where in Doppler frequency the target will appear at thenext instant of time; the estimated prediction being derived from a nextpredicted sweep value, and the next predicted range and closing velocityfrom object to target; the estimated prediction allowing the object toposition its Doppler frequency tracker to the next frequency location inpreparation to acquire the next target signal sample.

While the invention has been described, disclosed, illustrated and shownin various terms of certain embodiments or modifications which it haspresumed in practice, the scope of the invention is not intended to be,nor should it be deemed to be, limited thereby and such othermodifications or embodiments as may be suggested by the teachings hereinare particularly reserved especially as they fall within the breadth andscope of the claims here appended.

1. A radar system comprising: An electronic transmitter adapted to emita non-linear swept electromagnetic FM signal, said non-linear sweptelectromagnetic FM signal having a waveform mathematically described bya second-order-polynomial; at least one reflected signal electronicsensor associated with an object whose range and closing velocity to atarget will be estimated, at least one of said at least one reflectedsignal electronic sensor being adapted to receive a reflected signal,said reflected signal corresponding to a non-linear sweptelectromagnetic signal having been reflected from said target; at leastone electronic waveform processor operatively associated with said atleast one of said at least one reflected signal electronic sensor andconfigured and programmed to process an apparent emitted signal and saidreflected signal to generate an estimate of said range from said objectto said target and an estimate of said closing velocity of said objectto said target; and a plurality of computer readable instruction modulesexecutably associated with said at least one electronic waveformprocessor, said plurality of computer readable instruction modulesincluding: at least one Doppler Adjust module; when run by saidelectronic waveform processor, said Doppler Adjust module causing saidat least one electronic waveform processor to generate an AdjustedDoppler function for at least one sweep; said Adjusted Doppler functionrepresenting apparent Doppler shift derived using a non-varying rangevalue; and at least one Linear Regression module; when run, said LinearRegression module causing said at least one electronic waveformprocessor to perform linear regression on said Adjusted Doppler functionto produce a best-fit Linearly Regressed function, the slope of saidLinearly Regressed function representing a first estimate of said rangeof said object to said target; a y-intercept of said Linearly Regressedfunction, when divided by krng, representing a first estimate of closingvelocity of said object to said target; the variance of said best-fitLinearly Regressed function representing Doppler variance.
 2. The radarsystem of claim 1 wherein said plurality of computer readableinstruction modules further comprises at least one Emitted SignalCharacteristics module; when run by said electronic waveform processor,said Emitted Signal Characteristics module causing said at least oneelectronic waveform processor to calculate predetermined aspects of saidapparent emitted signal corresponding to said non-linear sweptelectromagnetic signal emitted from said electronic transmitter.
 3. Theradar system of claim 2 wherein said predetermined aspects of saidnon-linear swept electromagnetic signal comprises: kdop; krng; anddelkrng.
 4. The system of claim 2 wherein said Emitted SignalCharacteristics module comprises a Quad Regression module.
 5. The radarsystem of claim 2 wherein said Emitted Signal Characteristics modulecomprises a Quad Deriv module.
 6. The radar system of claim 1 whereinsaid non-varying range value is said range value of a last sample insaid at least one sweep.
 7. The radar system of claim 1 wherein saidplurality of modules further comprising a Variance module; when run bysaid electronic waveform processor, said Variance module causes saidelectronic waveform processor to produce an estimate of variance of saidfirst estimate of range of said object to said target using amathematical relation of measured Doppler to range.
 8. The radar systemof claim 7 wherein said Variance module, when run by said electronicwaveform processor, further causes said electronic waveform processor toproduce an estimate of variance of said first estimate of closingvelocity of said object to said target using a mathematical relation ofmeasured Doppler to closing velocity.
 9. The radar system of claim 8wherein said plurality of modules further comprises at least oneRefining Module; when run by said electronic waveform processor, saidRefining module causes said electronic waveform processor to produce arefined estimate of range and a refined estimate of closing velocityusing said first estimate of range of said object to said target, saidfirst estimate of closing velocity of said object to said target, saidestimate of variance of said first estimate of range, and said estimateof variance of said first estimate of closing velocity.
 10. The radarsystem of claim 9 wherein said at least one Refining Module is a Kalmanfilter.
 11. The radar system of claim 9 wherein said plurality ofmodules further comprises a Dop Com module; when run by said electronicwaveform processor, said Dop Com module causing said electronic waveformprocessor to provide an estimated prediction of where in Dopplerfrequency said target will appear at a next instant of time; saidestimated prediction being derived from a next predicted sweep value,and a next predicted range and closing velocity from said object to saidtarget; said estimated prediction allowing said object to position itsDoppler frequency tracker to a next frequency location in preparation toacquire a next target signal sample.
 12. A radar tracking method,comprising: transmitting a non-linear swept electromagnetic FM signalusing a transmitter, said non-linear swept electromagnetic FM signalhaving a waveform mathematically described by a second-order-polynomial;receiving a reflected signal at a reflected signal electronic sensorelectromechanically associated with said object, said reflected signalcorresponding to said non-linear swept electromagnetic FM signal havingbeen reflected from a predetermined target; generating an estimate of arange from said object to said predetermined target and an estimate of aclosing velocity of said object and said predetermined target byelectronically processing, on an electronic waveform processor, saidreflected signal and an apparent emitted signal corresponding to saidnon-linear swept electromagnetic signal emitted from said transmitter;running a Doppler Adjust module on said electronic waveform processor;when run, said Doppler Adjust module causing said at least oneelectronic waveform processor to generate an Adjusted Doppler functionfor at least one sweep; said Adjusted Doppler function representingapparent Doppler shift derived using a non-varying range value; andrunning a Linear Regression module on said electronic waveformprocessor; when run, said Linear Regression module causing said at leastone electronic waveform processor to perform linear regression on saidAdjusted Doppler function to produce a best-fit Linearly Regressedfunction, said slope of said Linearly Regressed function representing afirst estimate of said range from said object to said target; ay-intercept of said Linearly Regressed function, when divided by krng,representing a first estimate of closing velocity of said object to saidtarget; said variance of said best-fit Linearly Regressed functionrepresenting Doppler variance.
 13. The radar tracking method of claim 12wherein said generating an estimate of said range from said object tosaid predetermined target and an estimate of said closing velocity ofsaid object and said predetermined target by electronically processing,on an electronic waveform processor, said reflected signal and anapparent emitted signal corresponding to said non-linear sweptelectromagnetic signal emitted from said transmitter comprises running aEmitted Signal Characteristics module on said electronic waveformprocessor, said Emitted Signal Characteristics module causing said atleast one electronic waveform processor to calculate predeterminedaspects of said apparent emitted signal.
 14. The radar tracking methodof claim 13 wherein said predetermined aspects of said non-linear sweptelectromagnetic signal emitted from said electronic transmittercomprises: kdop; krng; and delkrng.
 15. The radar tracking method ofclaim 13 wherein said Emitted Signal Characteristics module comprises aQuad Regression module.
 16. The radar tracking method of claim 13wherein said Emitted Signal Characteristics module comprises a QuadDeriv module.
 17. Said radar tracking method of claim 12 wherein saidnon-varying range value is said range value of a last sample in said atleast one sweep.
 18. The radar tracking method of claim 12 furthercomprising running a Variance module on said electronic waveformprocessor; when run by said electronic waveform processor, said Variancemodule causes said electronic waveform processor to provide an estimatedvariance of said first estimate of range of said object to said targetusing a mathematical relation of measured Doppler to range and anestimate of variance of said first estimate of closing velocity of saidobject to said target using a mathematical relation of measured Dopplerto closing velocity.
 19. The radar tracking method of claim 18 furthercomprising running at least one Refining Module; when run by saidelectronic waveform processor, said Refining module causing saidelectronic waveform processor to produce a refined estimate of range anda refined estimate of closing velocity using said first estimate ofrange from said object to said target, said first estimate of closingvelocity of said object and said target, said estimate of variance ofsaid first estimate of range, and said estimate of variance of saidfirst estimate of closing velocity.
 20. The radar tracking method ofclaim 19 further comprising running at least one Dop Com module; whenrun by said electronic waveform processor, said Dop Com module causingsaid electronic waveform processor to provide an estimated prediction ofwhere in Doppler frequency said target will appear at a next instant oftime; said estimated prediction being derived from a next predictedsweep value, and a next predicted range and closing velocity from saidobject to said target; said estimated prediction allowing said object toposition its Doppler frequency tracker to a next frequency location inpreparation to acquire a next target signal sample.